So cities should remove all parking minimum laws, and let apartments and businesses decide how much parking to build. That's exactly what the article is saying.
Instead of investing money in parking, they could have spent that money on private buses, public bus passes for employees, bike parking, bike subsidies, Uber subsidies, sponsored carpools, bike paths, or nearby high density corporate housing.
As for freeway capacity, if we reduce free parking, that will cause less people to drive, making the freeways more clear.
So the natural response to that is to force businesses to have greater value? Is this not exactly what market forces would do naturally? A business with insufficient parking would have less value than one with, and would therefore compete less effectively.